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High-performance real-time systems are becoming increasingly common in several application domains, including automotive, robotics, and embedded. To meet the growing performance requirements of the emerging applications, these systems often adopt a heterogeneous System-on-Chip hardware architecture comprising multiple high-performance CPUs and one or more domain-specific accelerators. At the same time, the applications running on these systems are subject to stringent real-time and safety requirements. Due to the non-deterministic execution model of the compute elements involved and the co-location of the workloads, which leads to contention of the shared hardware resources, designing and orchestrating such applications is particularly challenging. In fact, the demand for novel methodologies, tools, and best practices to assist application designers working on high-performance real-time systems has never been stronger. To stimulate innovation in this area, this document outlines an industrial case study from the automotive domain targeting an Arm-based hardware platform. The selected application is an augmented reality head-up display, which can be considered a representative example of a high-performance real-time use case. This case study will serve as the basis for a (multi-year) challenge involving real-time and embedded systems researchers across academia and industry that will be kicked off at the 34superscript{th} Euromicro Conference on Real-Time Systems (ECRTS) 2022.